Can't mount second external drive after failed eject time machine backup

This morning my time machine disk (I'll call it drive A) failed to eject properly. I got a message that one of the files was in use but didn't see it and disconnected.

After this, I connected another external drive (I'll call that one drive B) which is FAT_32 formatted storage, not the time machine disk. This froze my system for a minute. After the system became responsive again, this drive B would not mount and showed greyed out in the disk utility. In an attempt to solve this:

- I rebooted (twice)

- I called apple care and they told me how to do PRAM and SMC reserts

- I called the drive manufacturer's helpdesk and they said the disk appeared to be OK but probably after the failed eject of the time machine on drive A the system somehow tried to identify drive B with the time machine (drive A). However they referred me back to apple. They knew of software tools to solve this for windows but not apple.

None of this solved my problem. It seems simple: drive B seems intact but cannot be mounted. Does anyone know what software I could use to 'correct' this problem? Disk utility is no help, since the disk cannot be mounted and all the repair and verify options are greyed out.

Thanks!